The Cut and Bayes posteriors can be replaced by distributions derived from the Posterior Bootstrap [1]} or Bagged posteriors [2]} and this suggests \(\delta \) -SMI-like sequences of distributions interpolating these “Cut" and "Bayes” distributions by adding “noise" with bandwidth \(\delta \)  to \(Y\) . Since these bootstrapped posterior distributions have good asymptotic Frequentist coverage of the pseudo-true parameters, at least for misspecified variance, it is to hoped that the \(\delta \) -SMI sequence would inherit these properties.
